Towards a Generalised Metaheuristic Model for Continuous Optimisation Problems

Abstract

Metaheuristics have become a widely used approach for solving a variety of practical problems. The literature is full of diverse metaheuristics based on outstanding ideas and with proven excellent capabilities. Nonetheless, oftentimes metaheuristics claim novelty when they are just recombining elements from other methods. Hence, the need for a standard metaheuristic model is vital to stop the current frenetic tendency of proposing methods chiefly based on their inspirational source. This work introduces a first step to a generalised and mathematically formal metaheuristic model, which can be used for studying and improving them. This model is based on a scheme of simple heuristics, which perform as building blocks that can be modified depending on the application. For this purpose, we define and detail all components and concepts of a metaheuristic (i.e., its search operators), such as heuristics. Furthermore, we also provide some ideas to take into account for exploring other search operator configurations in the future. To illustrate the proposed model, we analyse search operators from four well-known metaheuristics employed in continuous optimisation problems as a proof-of-concept. From them, we derive 20 different approaches and use them for solving some benchmark functions with different landscapes. Data show the remarkable capability of our methodology for building metaheuristics and detecting which operator to choose depending on the problem to solve. Moreover, we outline and discuss several future extensions of this model to various problem and solver domains.

Global Optimisation through Hyper-Heuristics: Unfolding Population-Based Metaheuristics

“…In the long run they are all heuristics that operate with different specifications. In the subsequent sections, we describe briefly these concepts, which were fully detailed in our previous manuscript [7]. Furthermore, since the majority of heuristics operate over a population (i.e., a set of agents), we need to lay some concepts: Definition 2 (Population).…”

“…For each step, it either returns to the search operator (h o ) or concludes the procedure, leading to h e . The signal-flow representation of metaheuristics is detailed in [7]. Now, consider a problem with a limited computational budget, which is common in real-world applications.…”

“…The most common ones are Single-point, Two-points, Uniform, Blend, and Linear crossover. Further information about the expressions corresponding to either pairing and crossover mechanisms can be found in [7,31].…”

“…Still, with the increasing appearance of proposals, it becomes exceedingly difficult to notice this issue. In our previous work, we analysed this situation and proposed a model to formally study metaheuristics pushing away the metaphors and only concentrating on their operative core [7]. However, we noticed that the standard metaheuristic model only comprises up to three simple heuristics or search operators, a fact strongly limiting their exploration and exploitation capabilities and making them highly susceptible to the No-Free-Lunch (NFL) [8] theorem.…”

“…Thus, it is essential to establish a standardised model, e.g., by using a generalised metaheuristic mould. We have taken a preliminary step in this direction by proposing a modelling scheme that allows merging Search Operators (SOs) from different metaheuristics [7]. Even so, it may be worthwhile to set up a branched model with different paths in such a way that different sets of SOs are applied to a given problem state to provide a more diverse behaviour.…”